Evaluate : `root3(4096/64)+3root3(3375/125)`

Options

A. 12
B. 13
C. -13
D. -12

Answer

To evaluate the expression \( \sqrt[3]{\frac{4096}{64}} + 3\sqrt[3]{\frac{3375}{125}} \), we will follow these steps:

### Step 1: Simplify \( \frac{4096}{64} \)
First, we need to simplify \( \frac{4096}{64} \).

\[ \frac{4096}{64} = 64 \]

### Step 2: Find the cube root of 64
Next, we find the cube root of 64.

\[ \sqrt[3]{64} = \sqrt[3]{4^3} = 4 \]

### Step 3: Simplify \( \frac{3375}{125} \)
Now, we simplify \( \frac{3375}{125} \).

\[ \frac{3375}{125} = 27 \]

### Step 4: Find the cube root of 27
Next, we find the cube root of 27.

\[ \sqrt[3]{27} = \sqrt[3]{3^3} = 3 \]

### Step 5: Multiply by 3
Now, we multiply the cube root of 27 by 3.

\[ 3\sqrt[3]{27} = 3 \times 3 = 9 \]

### Step 6: Add the results
Finally, we add the results from Step 2 and Step 5.

\[ 4 + 9 = 13 \]

### Final Answer
Thus, the evaluated expression is:

\[ \boxed{13} \]